It really does pay in the long run to practise the Doppio movimento painstakingly slowly and precisely, hands separately to start with, focussing from the outset on bringing the melody line out in a cantabile style. Do not be tempted to play it any faster than you can comfortably play it at any given point in the practice process. Very gradually build up the speed, maybe over weeks rather than days.
(Of course this is fairly obvious and nothing new, but the timescale for mastering a piece of any length really does depend on how much practice you can fit in each day, and how many other pieces you are learning at the same time, not to mention the efficiency of your practice. Building up a new recital will inevitably mean having several pieces on the go. It is important to do at least some practice on every piece each day. The danger otherwise is that a neglected piece will lose momentum and deteriorate.)
Choice of fingerings in the right hand of Op.48 no.1 in particular is also crucial so that extra 'weight' can be given to those notes which constitute this melody line. All the same notes need to come out clearly in the Doppio Movimento as in the original version of the melody in the first Lento section.
Indeed it is helpful to learn this slow section first so that you gain a perfect feel for how the melody notes are placed, and where the all important rests come. Then you can emulate this in the Doppio M. section. In this faster section, your right hand 5th finger will do a lot of the work (but not all of course) with regard to weighting the notes to bring out a cantabile tone. Try the suggested fingerings given, but adjust them according to what feels natural and comfortable for you. What edition are you using? I have the Paderewski edition in front of me now, but I am familiar with Urtext and others. The fingerings are invariably Chopin's own suggestions. He, like Beethoven, was pretty meticulous in this regard, but Chopin had fairly small hands and knew that fingering suggestions were just that, suggestions, and by no means set in stone. Getting the fingerings right for you (remember, feeling natural and comfortable to you) at the very outset is crucial; so that, even when you increase the tempo you are still in control of both that beautiful melody line and the agitato accompaniment.
Always feel free to experiment with alternative fingerings in any piece, but then stick to your final choices in all future practice, rather than swapping about as this just causes confusion in the memorisation process. I always have a pencil and eraser on my piano for this purpose as I occasionally change my mind in terms of finger choices. But eventually I make myself stick to my final selections, knowing that I have explored a range of suitable alternatives.
Appropriate and consistent fingerings in Op.48 no.1 will avoid the issue of missing out notes, particularly in the complex texture of the Doppio Movimento.
I hope this helps in some way, however small. If I can help in any other way as your practice evolves over the next days and weeks just say! Good luck. This is a wonderful piece which is very close to my heart. I first heard it when I was 6 on an LP my father regularly listened to of a Chopin recital by Stefan Askenase, teacher of a few great pianists including Martha Argerich.